how do web tools show my public IP address?

hi everyone, i'm totally new to this forum and also to building web tools, so apologies if this is a dumb question!

• i just launched a super basic "what is my ip" website, like the ones you see everywhere.
• i'm trying to understand the actual technical process for how my server gets the user's public IP address to display it back to them.
• is it just reading HTTP headers? or is there some more complex magic happening?
• also, are there any common pitfalls or privacy things i should be aware of when running such a tool?
• i'm really just trying to learn teh basics here.

thanks in advance!